It is well known that in his logical writings Leibniz typically disregarded the operation of disjunction, confining himself to the theory of conjunction ajid negation. Now, while this fact has been interpreted by Couturat and others as indicating a serious incompleteness of the Leibnizian calculus, it is shown in this paper that actually Leibniz's conjunction-negation logic, with 'est Ens', i. e. 'is possible' as an additional logical operator, is provably equivalent to Boolean algebra. Moreover, already in the Generales Inquisitiones of (...) 1686 Leibniz had established all basic principles that are necessary for a complete axiomatization of "Boolean" algebra. In this sense Leibniz should be acknowledged as the true inventor of the algebra of sets. (shrink)

Leibniz's development of a "calculus universalis" stands and falls with his theory of negation. During the entire period of the elaboration of the algebra of concepts, L1, Leibniz had to struggle hard to grasp the difference between propositional and conceptual negation. Within the framework of syllogistic, this difference seems to disappear because 'Omne A non B' may be taken to be equivalent to ‘Omne A est non-B’. Within the "universal calculus", however, the informal quantifier expression 'omne' is to be dropped. (...) Accordingly, ‘A non est B' expresses only the propositional negation of ‘A est B' and is hence logically weaker than ‘A est non-B'. Besides Leibniz's cardinal error of confusing propositional and conceptual negation the following issues are dealt with in this paper: -"Aristotelian" vs. "Scholastic" Syllogistic; – Metalinguistic theory of the truth-predicate; -Individual-concepts vs. concepts in general. (shrink)